A study of gravitational and magnetic effects on coupled stress bi-phase liquid suspended with crystal and Hafnium particles down in steep channel

A supercritical two-phase flow model suspended with crystal and Hafnium particles through a steep channel is proposed. The couple stress is used as a base liquid. The simultaneous effects of magnetic and gravitations imparting on the oblique flow are investigated. The non-linear leading equations governing the flow model are first reduced to ordinary system of differential equations and then the analytical method is invoked to find the closed form solution of the non-dimensional resulting equations. As a special case, the physical properties of two phase viscosity treatments for basaltic magma flow are taken into account and found in good agreement with the existing literature. The impact of pertinent variables of interest on the flow quantities is inspected graphically. •A couple stress fluid flow with crystal and Hafnium particles in a steep channel is analyzed.•Gravitational and magnetic effects are taken into account.•The supercritical basaltic magma flow is considered as a special case of proposed model.•The analytical method is invoked to find the closed form solutions.•The impact of pertinent variables is inspected graphically.